THE  OPTICAL  CONSTANTS  OF 
SODIUM  AND  POTASSIUM 


A THESIS 

Presented  to  the  Faculty  of  Philosophy  of  the  University 
of  Pennsylvania  in  Partial  Fulfilment  of 
the  Requirements  for  the  Degree 
of  Doctor  of  Philosophy 


By 

R.  W.  and  R.  C.  DUNCAN 


IReprinted  from  the  Physical  Review,  N.S.,  Vol.  I.,  No.  4,  April,  1913.] 


Digitized  by  the  Internet  Archive 
in  2017  with  funding  from 

University  of  Illinois  Urbana-Champaign  Alternates 


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THE  OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 

By  R.  W.  and  R.  C.  DUNCAN. 


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Reprinted  from  the  Physical  Review,  N.S.,  Vol.  I.,  No.  4,  April.  1913.) 


THE  OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 

By  R.  W.  and  R.  C.  Duncan. 

Introduction. 

TOURING  the  early  part  of  the  nineteenth  century  it  was  found  that 
light  was  partially  polarized  by  reflection  from  the  polished  sur- 
face of  a metal,  and  also  that  plane  polarized  light  became,  in  general, 
elliptically  polarized  upon  reflection  from  such  a surface.  Later  this 
was  shown  to  be  due  to  a relative  change  in  the  phase  of  the  two  com- 
ponents. The  amount  of  this  change  was  first  measured  in  1847  by 
Jamin,1  who  was  thus  enabled  to  calculate,  theoretically,  the  index  of 
refraction  of  the  metal  used.  The  next  important  work  along  this  line 
was  done  by  P.  Drude,2  who,  about  1890,  completed  a series  of  measure- 
ments from  which  he  determined  the  optical  constants  of  most  of  the 
common  metals.  • 

A large  amount  of  work  has  since  been  done,  so  that  at  the  present  time 
the  optical  constants  of  almost  all  of  the  metals  are  known,  with  the 
exception  of  a few  of  the  more  highly  oxidizable  ones.  On  account  of 
the  rapid  oxidation  of  these,  the  difficulty  has  been  to  obtain  a bright 
metallic  surface  and  to  preserve  it  long  enough  to  examine  its  optical 
properties.  The  few  attempts  that  have  been  made,  while  not  at  all 
satisfactory,  have  shown  that  these  metals  offer  an  interesting  field  for 
further  investigation.  In  1898  Drude3  made  a single  measurement  with 
sodium  light  reflected  from  the  molten  surface  of  metallic  sodium.  This 
measurement  gave  an  index  of  refraction  of  0.0045  which,  if  correct,  means 
that  light  travels  220  times  as  fast  in  that  metal  as  in  air.  After  making 
due  allowance  for  some  possible  errors,  which  Drude  admits  might  have 
lowered  his  result,  he  says  that  the  index  could  not  be  greater  than  0.054. 
But  this  value  is  still  remarkably  low  compared  to  the  indices  of  other 
metals. 

Since  Drude’s  value  of  the  index  of  sodium  was  made  with  sodium 
light,  the  question  arises  is  there  any  connection  between  the  low  value 
of  the  index  and  the  fact  that  the  light  used  was  of  a wave-length  peculiar 

1 Ann.  Chim.  Phys.  (3),  Vol.  19,  p.  296,  1847. 

2 Ann.  d.  Phys.,  Vol.  39,  p.  481,  1890. 

3 Ann.  d.  Phys.,  Vol.  64,  p.  159,  1898. 


295 


No  4 ] OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 

to  that  emitted  by  the  sodium  molecule.  Might  this  be  a phenomenon 
akin  to  resonance,  or  is  the  value  of  the  index  equally  low  for  all  colors? 
These  questions,  together  with  the  extraordinarily  low  index  obtained  by 
Drude,  suggested  the  investigation  reported  on  the  following  pages. 

The  Preparation  of  the  Surface. 

In  his  work  with  sodium,  Drude  obtained  a bright  metallic  surface 
by  melting  the  metal  in  an  atmosphere  of  rarified  hydrogen,  but  found 
it  necessary  to  renew  the  surface  every  few  minutes  on  account  of  its 
rapid  oxidation.  During  one  of  these  attempts  to  remove  the  thin  layer 
of  oxide  the  vessel  containing  the  sodium  was  broken  and  he  was  unable 
to  verify  his  first  determination.  In  the  present  investigation  a number 
of  preliminary  experiments  were  made  to  find,  if  possible,  a method  of 
obtaining  a more  permanent  surface,  free  from  oxide.  As  the  metal  can 
be  kept  indefinitely  under  oil,  it  seemed  possible  that  a bright  surface 
might  be  obtained  and  preserved  by  melting  the  metal  under  some 
light  transparent  oil.  The  attempts,  however,  were  not  satisfactory  for, 
while  a bright  surface  could  be  obtained  in  this  way,  it  would  remain 
bright  but  a few  minutes.  Then  again  on  account  of  the  large  surface 
tension  and  small  density  of  sodium,  the  molten  surface  assumed  a shape 
almost  spherical,  so  that  a comparatively  large  surface  would  be  required 
in  order  to  obtain  a small  part  of  the  surface  approximately  plane. 

Some  efforts  were  made  to  obtain  the  desired  surface  by  melting  the 
sodium  in  a vacuum,  but  here,  too,  it  was  difficult  entirely  to  prevent 
oxidation.  It  was  noticed,  however,  that  bright  surfaces  were  often 
obtained  against  the  inside  wall  of  the  glass  container.  These  surfaces 
remained  bright  after  the  sodium  had  solidified  and  could  be  preserved 
indefinitely  by  filling  the  vessel  with  dry  air  or  oil.  This  suggested  the 
possibility  of  obtaining  a permanent  sodium  mirror  against  a plane  glass 
plate.  With  this  end  in  view  a number  of  experiments  were  made. 
Many  of  these  ended  in  complete  failure,  but  others  gave  more  promising 
.results.  Finally,  by  combining  and  improving  several  plans,  a method 
was  devised  which  has  proved  quite  satisfactory. 

The  Method  in  Brief. — A little  box,  or  capsule  (Fig.  2),  was  made  by 
cementing  two  plane  glass  plates  to  the  ends  of  a short  iron  tube,  or 
ring,  from  the  side  of  which  a small  glass  tube  extended.  The  latter  tube 
was  about  5 cm.  long  and  at  its  outer  end  was  drawn  out  so  as  to  leave 
a very  small  opening.  This  capsule  was  suspended  in  a cylindrical 
glass  vessel,  in  the  lower  end  of  which  had  been  placed  some  metallic 
sodium.  The  vessel  was  then  closed  and  evacuated  and  the  lower  end 
immersed  in  an  oil  bath,  which  was  heated  to  a temperature  of  about 


296 


R.  W.  AND  R.  C.  DUNCAN. 


Second 

Series. 


iio°  C.  Meanwhile  the  suspended  capsule  was  being  heated  up  to 
approximately  the  same  temperature  by  an  electric  current  passing 
through  resistance  grids  held  against  the  glass  ends.  When  the  sodium 
below  had  melted  the  capsule  was  lowered  until  the  small  end  of  the 
glass  tube  dipped  into  the  molten  metal.  Then  by  admitting  dry  air 
into  the  containing  vessel  the  liquid  sodium  was  forced  up  through  the 
glass  tube  into  the  capsule  and  pressed  firmly  against  the  plane  glass  ends, 
thus  forming  two  bright  sodium  mirrors.  After  the  whole  apparatus 
had  been  allowed  to  cool,  the  sodium  capsule  was  taken  out,  the  small 
glass  tube  removed,  and  the  opening  closed  with  paraffin.  In  this  con- 
venient form  the  sodium  mirrors  could  be  kept  indefinitely.  The  method 
was  found  to  work  equally  well  with  potassium,  and  all  sodium  or  potas- 
sium surfaces  studied  were  obtained  in  this  way. 

Apparatus.  — The  containing  vessel 
was  made  of  glass  and  consisted  of  two 
parts  {A  and  B , Fig.  1)  fitting  together 
at  a in  a ground  junction.  The  lower 
part  A was  made  by  sealing  the  tube  D, 

5 cm.  long  and  1.5  cm.  in  diameter  and 
closed  at  one  end,  into  the  larger  tube  C, 

7 cm.  long  and  4 cm.  in  diameter.  The 
upper  part  B,  9 cm.  long  and  4 cm.  in 
diameter,  was  made  from  a glass  tube 
closed  at  one  end.  At  / was  sealed  in 
a side  tube,  which  ended  in  the  ground 
cone  h.  A glass  rod  E carried  a cone  d 
ground  to  fit  h , and  by  means  of  the  T- 
shaped  end  H,  could  be  rotated  about 
the  line  cd  as  an  axis.  It  thus  served  as 
a windlass  to  raise  and  lower  the  capsule 
F which  was  suspended  by  a cord  wrap- 
ped around  the  rod  at  c.  The  wires,  carrying  the  current  used  to  heat . 
the  capsule,  were  led  in  through  the  small  tube  e,  which  was  closed  with 
sealing  wax.  A rubber  tube  connected  the  outlet  Ho  a two-way  stop- 
cock, one  branch  of  which  led  to  the  air-pump,  while  the  other,  through 
drying  tubes,  led  to  the  outside  air.  The  vessel  A B could  thus  either 
be  evacuated  through  k , or  when  evacuated,  could  be  refilled  with  dry 
air  through  the  same  tube. 

The  short  iron  tube  ( R , Fig.  2)  used  in  making  the  capsule,  was  0.8 
cm.  in  length  and  1.5  cm.  in  diameter.  A hole  a 0.45  cm.  in  diameter  was 
drilled  radially  through  the  side  of  the  tube  midway  between  the  ends. 


297 


No1"/*]  OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 

A fillet  5 0.08  cm.  wide  and  of  the  same  depth  was  cut  around  the  outside 
edge  of  each  end,  thus  leaving  the  shoulder  t on  the  inside  edge.  The  end 
faces  of  these  shoulders  were  made  as  plane  as  possible  by  grinding  on 
fine  emery  paper  backed  by  a surface  plate.  The  two  pieces  of  plane 
glass  gg,  after  being  carefully  cleaned,  were  clamped  tightly  against 
these  shoulders.  The  fillet  along  the  outside  edge  of  the  metal  ring, 
together  with  the  adjacent  glass  plate,  now  formed  a little  groove  which 
was  filled  with  cement,  while  the  shoulder  pressing  against  the  glass 
prevented  the  cement  from  creeping  inside.  The  capsule  was  completed 


Fig.  2.  Fig.  3. 


by  cementing  the  side  tube  T into  the  opening  a.  It  was  then  baked  at 
a temperature  of  about  120°  C.  for  several  hours,  until  the  cement,  which 
was  at  first  a light  yellow,  became  dark  brown.  In  some  cases  a tube  of 
brass  (S,  Fig.  3)  was  used  for  the  side  tube  T.  It  was  made  from  a brass 
rod,  0.45  cm.  in  diameter  and  5 cm.  long,  which  was  tapered  at  one  end 
almost  to  a point.  A hole  0,  0.3  cm.  in  diameter,  was  drilled  along  the 
axis  of  the  rod  to  the  point  n.  Then  a very  small  hole  0.03  cm.  in  diameter 
was  drilled  from  m to  n , to  connect  with  the  larger  opening. 

Precautions  to  Prevent  Oxidation. — As  the  most  difficult  problem  in  the 
whole  research  was  the  obtaining  of  a surface  free  from  oxide,  the  pre- 
cautions taken  to  prevent  oxidation  will  be  described  in  some  detail. 

In  preparing  to  make  a mirror,  the  containing  vessel  AB  was  first 
thoroughly  cleaned.  It  was  then  placed  in  an  upright  position,  and  the 
capsule  ( F , Fig.  1)  suspended  from  the  rod  E as  already  described.  The 
vessel  was  alternately  evacuated  and  filled  with  dry  air1  a number  of 
times,  in  order  to  remove  any  water  vapor  or  other  gases  from  the  interior. 
Finally  it  was  left  closed,  full  of  dry  air.  The  vessel  was  further  protected 
from  moisture  by  a U-tube  of  phosphorus  pentoxide,  placed  between  it 
and  the  pump.2 

1 The  air  was  dried  by  drawing  it  through  U-tubes  of  sulphuric  acid  and  phosphorus 
pentoxide. 

2 Gaede’s  combination  of  oil  and  mercury  pumps  was  used. 


298 


R.  W.  AND  R.  C.  DUNCAN. 


Second 

.Series. 


The  quantity  of  sodium,  a part  of  which  was  to  be  used  in  making  the 
mirror,  was  immersed  in  a light  paraffin  oil.  By  means  of  a cork 
borer  of  a diameter  just  smaller  than  that  of  the  tube  ( D , Fig.  1),  a 
cylindrical  stick  about  3 cm.  long  was  cut  out  of  the  metal.  Any  heavy 
coating  of  oxide  still  adhering  to  the  ends  of  the  stick  was  removed  with 
a knife.  The  cylinder  of  sodium,  thus  obtained,  was  quite  free  from 
oxide,  since  all  the  cutting  had  been  done  under  oil.  The  stick  was  lifted 
out  and  rinsed  thoroughly  in  benzine  to  remove  the  oil,  the  benzine,  in 
turn,  being  removed  by  rinsing  in  toluene.  Now,  as  quickly  as  possible, 
the  glass  vessel  AB  was  opened,  the  sodium  cylinder  dropped  into  the 
receptacle  D , and  the  vessel  immediately  closed  and  evacuated.  The 
remaining  toluene  was  therefore  rapidly  removed  by  evaporation  at  a 
reduced  pressure.  It  will  be  noted  that  at  no  time  during  the  whole 
process  was  the  sodium  exposed  to  the  open  air.  In  spite  of  all  these 
precautions,  however,  a surface  film  of  oxide  would  always  form  before 
the  sodium  was  entirely  melted.  Therefore,  in  order  to  pierce  this 
surface  film,  and  to  permit  as  little  as  possible  of  it  from  entering  the 
capsule,  it  was  necessary  to  make  the  tube  (T,  Fig.  2)  pointed,  with  a 
very  small  opening  in  the  end  (as  already  described). 

It  was  possible  in  this  way  to  obtain  bright  surfaces,  but,  upon  a 
close  examination,  they  proved  to  be  covered  with  an  extremely  thin 
filmy  veil.  This  film,  however,  was  not  spread  uniformly  over  the 
surface,  but  was  distributed  in  curved  and  ring-like  figures,  leaving  in  a 
number  of  cases,  small  areas  which  were  entirely  free  from  it.  Further 
experiment  proved  that  this  thin  film  was  due  to  a spreading  out  of  a 
small  quantity  of  oxide  which  had  entered  the  tube  T when  it  broke 
through  the  surface  of  the  molten  metal. 

In  order  to  prevent  this,  two  methods  were  used  with  about  equal 


Fig.  4.  Fig.  5. 


success.  In  the  first  method  a wedge-shaped  device  was  used  to  cut 
the  surface  film  and  open  a way  through  it  for  the  tube  T.  This  device 
(Fig.  4)  was  made  by  fastening  two  very  thin  flat  steel  springs  pp,  each 
1.3  cm.  long  and  0.5  cm.  wide,  to  the  metal  disk  d so  that  the  outer  ends 
of  the  springs  were  held  together,  thus  making  a sort  of  hollow  wedge 
as  shown  in  the  figure.  A hole,  0.6  cm.  in  diameter,  was  drilled  through 


299 


NoL4.  J optical  constants  of  sodium  and  potassium. 

the  center  of  the  disk,  which  was  1.2  cm.  in  diameter,  just  smaller  than 
the  inside  diameter  of  D (Fig.  1).  This  was  suspended  from  the  capsule 
so  that  the  tube  T extended  through  the  hole  in  the  disk,  with  the  pointed 
end  inside  the  hollow  wedge.  Now  as  the  capsule  was  lowered,  the  wedge 
pierced  the  oxide  film  and  entered  the  sodium,  stopping  when  the  disk 
rested  upon  the  surface  of  the  metal.  By  a further  lowering  of  the  cap- 
sule, the  sides  of  the  wedge  were  forced  apart  by  the  pointed  tube.  This 
pushed  aside  the  surface  film  so  that  the  point  of  the  tube  could  enter 
directly  the  bright  surface  of  the  metal. 

In  the  second  method  a glass  tube  (W,  Fig.  5),  whose  outside  diameter 
was  slightly  less  than  the  inside  diameter  of  the  receptacle  D , was  drawn 
down  at  one  end  to  an  opening  h about  0.8  cm.  in  diameter.  This  tube 
was  then  suspended,  small  end  downward,  from  the  capsule  (F,  Fig.  1), 
so  that  the  lower  end  of  the  tube  W was  about  1 cm.  below  the  point  m 
of  the  small  tube  T.  When,  upon  lowering  this  contrivance,  the  lower 
end  of  W reached  the  metal  some  of  the  surface  film  would,  of  course, 
enter  at  h . As  the  tube  W continued  to  descend,  the  liquid  metal, 
entering  through  h from  bolow,  burst  through  and  pushed  aside  this  film 
(which  adhered  to  the  sides  of  the  tube  W),  thus  permitting  the  point  of 
the  tube  T to  enter  a bright  globule  of  melted  sodium. 

Both  of  these  devices  were  of  considerable  help  in  obtaining  bright 
surfaces,  but  neither  could  be  said  to  be  consistently  successful.  By 
making  a number  of  mirrors,  however,  a few  were  obtained  which  were 
practically  free  from  this  surface  film.  The  results  given  in  this  report 
were  obtained  from  these  surfaces. 

Other  Surface  Defects. — In  some  cases  the  surface  of  the  mirror  was 
found  to  be  marred  by  numerous  fine  lines  along  which  the  sodium 
seemed  to  have  drawn  away  from  the  glass.  These  lines  suggested  a 
crystalline  formation  and  probably  had  been  caused  by  the  contraction 
of  the  sodium  upon  solidifying.  This  configuration  on  the  surface  was 
especially  noticeable  when  the  mirror  was  examined  with  polarized  light, 
for,  since  the  light  totally  reflected  from  the  back  surface  of  the  glass 
along  these  lines  differed  in  phase  from  that  reflected  from  the  sodium 
surface,  both  could  not  be  extinguished  at  the  same  time.  Fortunately, 
however,  only  a few  of  the  mirrors  showed  this  defect,  and  they  were  either 
entirely  discarded  or  measurements  made  only  on  that  part  of  the  surface 
from  which  these  lines  were  entirely  absent. 

A number  of  failures  proved  that  unless  the  glass  plates,  upon  which 
the  mirrors  were  to  be  formed,  were  heated  to  approximately  the  tem- 
perature of  the  melted  sodium,  the  metal  would  solidify  as  soon  as  it 
touched  the  plates,  leaving  streaks  or  striations  across  the  surface. 


R.  W.  AND  R.  C.  DUNCAN. 


Seconl 

.Series. 


300 

It  was  also  found  necessary  to  heat  the  tube  T , through  which  the  sodium 
was  forced  up  into  the  capsule,  for,  otherwise  the  sodium  would  solidify 
while  yet  in  the  tube,  and  so  never  reach  the  glass  plates.  On  this  account 
a brass  tube  proved  much  more  convenient  than  the  glass  one  originally 
used,  since  the  whole  of  the  brass  tube  could  be  heated  by  merely  heating 
the  capsule. 

Cement. — In  making  the  capsule  quite  a little  difficulty  was  experienced 
in  finding  a satisfactory  cement,  i.  e.,  one  which  would  fasten  together 
glass  and  iron  in  an  air-tight  junction  and  would  not  soften  or  become 
porous  when  heated  in  a vacuum  to  the  required  temperature  (about 
iio°  C.).  A number  of  cements  were  tried,  some  being  commercial 
products,  while  others  were  mixed  in  the  laboratory  according  to  various 
formulae.  The  one  finally  selected  is  on  the  market  under  the  trade  name 
“ Rock  Cement.”  When  first  tried,  this  was  used  according  to  the  printed 
directions,  but  was  not  satisfactory.  Further  experiment,  however, 
showed  that  it  could  be  made  so  if  thoroughly  dried  by  heating.  It  was 
also  noticed  that  better  results  were  obtained  by  allowing  the  cement  to 
thicken  somewhat  by  evaporation  before  using. 

Measurements. 

Method  and  Apparatus. — Drude’s  method  for  obtaining  the  optical 
constants  of  metals  was  used  throughout  this  investigation.  It  consists 
in  an  examination  of  polarized  light  reflected  from  the  polished  surface 
of  the  metal.  If  the  incident  light  be  polarized  in  a plane  making  an 
angle  of  450  with  the  plane  of  incidence,  the  quantities  to  be  measured 
are  0,  the  angle  of  incidence;  A,  the  phase  change  introduced  by  reflec- 
tion; and  0,  the  azimuth  of  restored  polarization.  The  optical  constants 
( n , the  index  of  refraction  and  k,  the  index  of  absorption)  are  obtained  by 
substitution  in  the  following  formulae,  given  by  Drude.1 

n2(i  — k 2)  = 5 2 cos  20  + sin2  0,  (1) 

2n2K  = S2  sin  20,  (2) 

where 

cos  2P  = sin  20  cos  A,  (3) 

tan  0 = tan  20  sin  A,  (4) 

S = sin  0 tan  0 tan  P.  (5) 

Writing 

S2  cos  20  + sin  0 = A,  (6) 

S2  sin  20  = B,  (7) 

then 

2n2  = s/A2  + B2  +A, 

^A2  + B2  - A. 

K — 


1 Ann.  d.  Phys.,  Vol.  64,  pp.  161-2,  1898. 


B 


(8) 

(9) 


VOL.  I.' 

No.  4.  . 


OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 


301 


The  principle  angle  of  incidence  </>,  the  principal  azimuth  and  the 
reflecting  power  R , are  given  by : 

sin4  <f>  tan4  0 = n4{i  + k2)2  — 2n2{i  — k2)  sin2  <f>  + sin4  </>,  (10) 

f = 14  tan"1 /c,  (11) 

n2{  1 + k2)  + 1 — 2n 
R = rc2(i  + k2)  + i + 2n 

Since  for  sodium  and  potassium  the  constant  A (Eq.  6)  is  negative, 
the  calculations  may  be  much  simplified.  Making  A negative  and 
expanding  the  radical,  equation  (8)  becomes 

/ B2  B4  \ 

2ni  = A\^~8Ai  + etC-}- 


As  B is  small  compared  to  A , all  terms  except  the  first  may  be  ne- 
glected. This  gives 

" ' rs-  (,3) 

In  a similar  way,  equation  (9)  may  be  simplified,  giving 


K = 


2A 

B' 


(h) 


In  all  calculations  made  in  this  report  an  error  of  less  than  one  per  cent, 
results  from  using  equations  (13)  and  (14). 

As  in  Drude’s  experiments,  the  instrument  used  was  a spectrometer 
fitted  with  a polarizing  and  an  analyzing  nicol  and  a Soleil-Babinet  com- 
pensator. The  desired  wave-length  was  obtained  by  means  of  a mono- 
chromatic illuminator,  the  source  of  light  being  an  electric  arc.  For  each 
particular  wave-length  used,  the  zero  position  and  the  constant  of  the 
compensator  were  accurately  determined. 

Since  the  formula  for  n involves  the  tangent  of  the  angle  2 \f/,  usually 
large,  a small  error  in  measuring  this  angle  has  a much  greater  effect 
upon  the  result  than  a corresponding  variation  in  A.  This  is  especially 
true  of  the  light  reflected  from  a sodium  surface,  for  which  21 p is  about  89°. 

A number  of  careful  measurements,  made  to  determine  the  most  accu- 
rate method  of  setting  the  nicol,  showed  that  the  best  results  were  ob- 
tained by  removing  the  eyepiece  of  the  telescope  and  looking  directly  at 
the  nicol.  Viewed  in  this  way,  there  appeared,  at  the  extinction  point, 
a broad  and  quite  black  horizontal  band  which  never  entirely  covered 
the  field.1  Upon  sliding  the  wedge  in  the  compensator  this  band  would 

1 This  is  not  the  phenomenon  so  often  noticed  with  crossed  nicols,  for  the  band  appeared 
only  when  the  compensator  was  in  position.  With  the  new  compensator  (mentioned  else- 
where in  this  article)  the  field  was  uniform,  but  if  the  quartz  plates  were  rotated  slightly  upon 
each  other,  the  band  appeared  and  became  quite  distinct. 


302 


R.  W.  AND  R.  C.  DUNCAN. 


Second 

.Series. 


move  up  or  down  in  the  field,  while  upon  slightly  moving  the  nicol  in 
either  direction  from  an  extinction  point,  it  would  slowly  fade  away, 
usually  moving  across  the  field  in  the  direction  of  its  length.  The  cause 
of  this  unexpected  appearance  of  the  field  has  been  traced  to  a fault  in 
the  construction  of  the  compensator,  the  principal  axes  of  the  quartz 
plates  not  being  exactly  perpendicular  to  each  other. 

The  extinction  point  for  both  the  compensator  and  the  nicol  was  taken 
to  be  that  position  for  which  the  dark  band  was  centered  in  the  field.  For 
the  compensator,  the  value  used  for  the  extinction  point  was  the  mean 
of  eight  or  ten  settings.  For  the  nicol,  a larger  number  of  readings  was 
necessary,  since,  under  the  best  conditions,  the  individual  settings  varied 
by  approximately  thirty  minutes  of  arc.  Therefore,  in  order  to  get 
readings  in  every  possible  position  of  both  the  polarizer  and  the  analyzer 
the  following  method  was  adopted.  The  polarizer  was  set  in  four  posi- 
tions, each  450  from  the  plane  of  incidence.  At  each  of  these  positions, 
seven  to  ten  readings  of  the  analyzer  were  taken  for  each  of  its  two  extinc- 
tion points,  i8o°  apart.  Therefore  the  value  obtained  for  2\p  was  the 
mean  of  50  to  80  readings.1 

Mounting  the  Mirrors. — The  mirrors  were  mounted  so  as  to  be  viewed 
through  a prism.  A drop  or  two  of  cedar  oil,  which  had  approximately 
the  same  index  of  refraction  as  the  glass,  was  placed  upon  the  surface 
of  the  mirror  and  the  mirror  pressed  firmly  against  the  hypotenuse  side 
of  a right-angled  prism.  The  light  entered  one  leg  of  the  prism  normally 
and,  after  reflection  at  the  sodium  surface,  emerged  normally  through 
the  other  leg.  By  this  plan  all  the  troublesome  reflections  from  the 
front  surface  of  the  glass  of  the  mirror  were  avoided,  and,  since  the  light 
was  normal  to  both  prism  faces,  it  suffered  no  change  of  phase  or  of 
azimuth,  either  at  the  point  of.  incidence  or  emergence.  In  order  to 
remove  any  film  of  grease  or  other  foreign  matter,  which  might  cause  a 
phase  change,  the  mirror  and  all  of  the  surfaces  of  the  prism  were  carefully 
washed  before  mounting. 

Tests  for  Possible  Corrections. — Should  there  be  a slight  difference 
between  the  value  of  the  refractive  index  of  the  cedar  oil  and  that  of  the 
glass,  a change  in  the  azimuth  of  polarization  would  be  produced  at  the 
boundary  between  the  two  media.  A test  for  such  an  effect  was  made 
in  two  ways,  as  follows: 

First,  a piece  of  plate  glass  was  fastened  with  the  cedar  oil  to  the 
hypotenuse  side  of  the  prism.  Polarized  light  was  sent  through  the 
prism  in  the  same  way  as  before,  but  was  now  totally  reflected  from  the 

1 A new  compensator  combined  with  a half  shadow  analyzer  (Zehnder,  Ann.  d.  Phys.,  Vol. 
26,  p.  985,  1908)  has  since  been  received  from  Germany,  and  the  few  measurements  taken  with 
it  agree  closely  with  those  reported  in  this  paper. 


303 


Nou  4-  J OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 

back  surface  of  the  glass  plate.  A careful  examination  of  this  light  which, 
it  will  be  noticed,  had  passed  twice  through  the  oil  film,  each  time  at  an 
angle  of  450,  showed  no  change  in  the  azimuth  of  polarization.  The 
phase  change  was  also  measured  and  found  to  agree  closely  with  that 
to  be  expected  from  total  reflection. 

Secondly,  five  square  pieces  of  glass,  cut  from  the  plate  used  in  making 
the  sodium  mirrors,  were  placed  between  6o°  prisms  as 
shown  in  Fig.  6.  A drop  of  cedar  oil  was  placed  between 
each  plate,  and  between  the  first  and  last  plates  and  the 
prism  faces,  and  the  whole  pressed  firmly  together.  Polarized 
light  was  sent  through  the  combination  in  such  a way  as 
to  pass  formally  through  the  outer  prism  faces  (as  indicated 
in  the  figure).  The  light  therefore  traversed  twelve  surfaces  Fig.  6. 
of  contact  between  glass  and  oil,  the  angle  at  each  being  6o°. 

Here  again  a careful  set  of  measurements  failed  to  show  any  change 
in  the  azimuth  of  polarization.  Hence,  any  effect,  if  present,  must  be 
negligible. 

Another  possible  source  of  error  was  the  presence  of  the  oxide  film, 
of  which,  as  already  mentioned,  almost  every  sodium  mirror  showed 
at  least  a trace.  In  order  to  determine  the  optical  effect  of  this  film, 
the  phase  change  and  restored  azimuth  were  measured  on  six  different 
sodium  mirrors.  A week  later  a second  set  of  measurements  were  made 
on  the  same  surfaces.  In  the  results,  which  are  given  below  (Table  I.), 
the  phase  change  is  expressed  in  head  divisions  of  the  micrometer  screw 
and  may  be  reduced  to  degrees  by  multiplying  by  0.3937.  The  numbers 
given  in  the  first  column  are  used  merely  to  distinguish  the  individual 
surfaces. 

Table  I. 


Mirror 

Phase  Change. 

Azimuth. 

No. 

1st. 

2d. 

Av. 

1st. 

2d. 

Av. 

1 

329 

327 

328 

89°  21' 

89°  23' 

89°  22' 

2 

322 

334 

328 

89°  20' 

89°  24' 

89°  22' 

3 

310 

306 

308 

89°  6' 

89°  13' 

89°  10' 

4 

320 

305 

312 

89°  3' 

88°  54' 

88°  58' 

5 

330 

329 

329 

88°  54' 

89°  3' 

88°  58' 

6 

316 

317 

317 

88°  50' 

89°  0' 

88°  55' 

The  results  have  been  arranged  in  the  above  table  in  descending  order 
of  the  average  azimuth,  and  an  examination  of  the  individual  surfaces 
showed  that  in  general  the  film  became  more  pronounced  in  the  same 
order.  No  such  variation  of  phase  change  could  be  observed.  A com- 


304 


R.  W.  AND  R.  C.  DUNCAN. 


| Second 
ISeries. 


parative  study  of  the  first  and  second  columns  in  both  the  phase  change 
and  azimuth  above  indicates  no  consistent  change  in  the  surfaces  during 
the  week  which  elapsed  between  the  two  sets  of  readings.* 1 

As  Nos.  i and  2 were  practically  free  from  film,  they  were  chosen  for 
the  determination  of  the  optical  constants  of  the  metal  as  given  below. 
It  is  believed  that  the  results  obtained  from  these  mirrors  are  very  near 
to  those  that  would  be  obtained  from  a perfect  surface,  since  the  rather 
heavy  film  on  Nos.  5 and  6 reduced  the  azimuth  by  less  than  thirty 
minutes. 

Nos.  1,  3 and  4 were  made  from  (Merck)  sodium,  guaranteed  to  be 
free  from  other  metals,  while  Nos.  2,  5 and  6 were  made  from  ordinary 
commercial  sodium.  The  results  did  not  show  any  consistent  difference 
between  the  two  specimens  of  the  metal. 

It  is  interesting  to  note  that  Nos.  5 and  6 were  mirrors  on  the  opposite 
sides  of  the  same  capsule.  No.  5 was  made  directly  on  the  hypotenuse 
face  of  a prism  (by  substituting  a prism  for  one  of  the  glass  plates  of  the 
capsule),  and  so  could  be  examined  without  the  use  of  the  oil  film,  while 
No.  6 was  formed  on  the  glass  plate  and  examined  through  the  oil.  The 
results  indicate  that  the  oil  film  had  no  appreciable  effect. 

Method  Applied  to  Mercury. — Exactly  the  same  method  was  used 
throughout  to  determine  the  optical  constants  of  mercury.  As  the  con- 
stants for  this  metal  are  well  known  the  results  (Table  II.)  serve  as  a 
check  upon  the  method.  It  will  be  noticed  that  the  values  for  n are 
slightly  higher  than  those  obtained  by  Drude2  or  by  Meier.3  This  may 
be  due  to  the  particular  specimen  of  mercury  used. 

Table  II. 

Mercury.  <f>  = 45°. 


A 


A 


2i p 


6,650 

5,893 

4,720 


162°  11' 
160°  4' 
156°  14' 


82°  57' 
83°  1' 
83°  18' 


2.34 
1.92 

1.35 


2.47 

2.78 

3.42 


Former  values  obtained  are : 

Drude,  X = 5,893,  n = 1.73,  k = 2.87. 

Meier,  X = 5,893,  n = 1.62,  k = 2.71. 

Specimen  Set  of  Readings  in  Detail. — In  order  to  give  an  idea  of  the 
accuracy  of  setting  and  the  method  of  procedure,  a complete  series  of 
readings,  taken  to  determine  a single  value  of  n and  k , is  given  in  Table 
III.  Every  result  was  determined  from  a similar  series  of  readings. 

1 Measurements  taken  on  some  of  these  surfaces  three  months  later  showed  no  change  in 
the  character  of  the  surface. 

2 Ann.  d.  Phys.,  Vol.  39,  p.  530,  1890. 

3 Ann.  d.  Phys.,  Vol.  31,  p.  1031,  1910. 


VOL.  1.1 

No.  4.  J 


OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM. 


305 


Table  III. 


A . Determination  of  Zero  Point  and  Constant  of  Compensator. 
Sodium  mirror  No.  1.  </>  = 44°  59', 


For  Phase  Difference  of 

— 2n 

Zero. 

+ 27T 

(0)  80.0 

(12)  37.0 

(23)  91.0 

81.0 

36.0 

95.0 

79.2 

36.0 

98.0 

81.0 

38.5 

99.0 

78.3 

38.0 

(24)  1.0 

81.0 

38.0 

(23)  95.0 

78.2 

36.5 

96.2 

Averages 

(0)  79.8 

(12)  37.0 

(23)  96.3 

Numbers  in  ( ) indicate  whole  number  of  turns  of  the  micrometer  screw.  The  readings 
are  in  head  divisions. 

2,316.5  divisions  = 720°  (4tt).  Therefore  1 div.  = 720/2,316.5  deg. 

B.  Determination  of  Phase  Change  upon  Reflection. 


Readings  for  Extinction 
At  Beginning.  At  End  of  Series. 


(16)  90.0 

(16)  81.5 

89.0 

83.0 

88.0 

84.2 

86.0 

84.0 

1,685.8  - 

- 1,237  = 448.8  divisions. 

86.5 

82.5 

87.2 

85.0 

88.6 

86.0 

Therefore  A = 

139°  29'. 

Av.  (16)  87.9 

(16)  83.7 

General  average,  1,685.8. 


C.  Determination  of  Restored  Azimuth. 


Polarizer. 

49° 

39' 

22gc 

5 39' 

Analyzer 

360°  9' 

179°  29' 

179°  48' 

359°  42' 

359°  22' 

179°  17' 

180°  7' 

359°  40' 

359°  30' 

180°  2' 

180°  31' 

359°  42' 

360°  20' 

179°  4' 

180°  32' 

359°  4' 

360°  8' 

179°  33' 

179°  46' 

359°  40' 

359°  59' 

179°  23' 

179°  44' 

359°  32' 

360°  11' 

179°  52' 

179°  40' 

359°  46' 

General  average  (reduced  to  one  position),  359°  46.2'. 


Polarizer. 

x39c 

’39' 

3I9C 

5 39' 

Analyzer 

270°  40' 

90°  53' 

90°  27' 

270°  1' 

270°  24' 

90°  9' 

90°  22' 

270°  14' 

270°  22' 

90°  18' 

90°  28' 

270°  53' 

270°  1' 

90°  32' 

89°  48' 

270°  11' 

270°  24' 

90°  28' 

90°  28' 

270°  31' 

270°  11' 

90°  9' 

89°  53' 

270°  10' 

270°  42' 

90°  19' 

90°  2' 

270°  54' 

306 


R.  W.  AND  R.  C.  DUNCAN. 


[Second 

LSeries. 


General  average,  270°  20.9'.  Therefore  2 = 89°  25.3'. 

By  substitution  A = — 3.1553,  B = 0.1135.  Giving  n = 0.032,  k = 55.6. 
Index  of  refraction  for  glass  plate  =1.5  (approximately).1 
Therefore  the  index  of  refraction  from  air  to  sodium  is: 

n = 1.5  X 0.032  = 0.048. 


Results. 

Table  IV. 

Sodium. 

Sodium  mirror  No.  1.  </>  = 44°  59'. 


A 

A 

2 . 

n 

l 

6,650 

139°  29' 

89°  25.3' 

0.048 

55.6 

5,893 

134°  46' 

89°  22.9' 

0.042 

54.3 

5,460 

130°  34' 

0 

CN 

OO 

0.045 

44.7 

4,720 

124°  34' 

89°  0' 

0.051 

34.2 

4,350 

117°  58' 

88°  46.7' 

0.053 

26.4 

Sodium  mirror  No.  2.  <f>  = 44°  59'. 


A 

A 

2 \p 

n 

1C 

6,650 

142°  1' 

89°  25.9' 

0.053 

54.5 

5,893 

137°  10' 

89°  24.7' 

0.045 

55.8 

5,460 

136°  6' 

89°  9.8' 

0.060 

40.6 

4,720 

130°  20' 

88°  57.5' 

0.062 

32.4 

4,350 

127°  7' 

88°  32.0' 

0.063 

37.0 

The  averages  from  the  above  are  given  in  the  second  and  third  columns 
below.  The  values  of  </>,  and  R , given  in  the  last  three  columns,  are 
obtained  by  using  these  averages  in  the  formulae  (io),  (i i) , and  (12). 


A 

n 

K 

<*> 

R 

6,650 

0.051 

55.0 

72°  11' 

44°  29' 

97.7 

5,893 

0.044 

55.0 

68°  51' 

44°  29' 

97.1 

5,460 

0.052 

42.6 

68°  48' 

44°  20' 

96.5 

4,720 

0.057 

33.3 

66°  29' 

44°  9' 

95.2 

4,350 

0.058 

31.7 

66°  0' 

44°  6' 

94.8 

Table  V. 


Potassium. 

Potassium  mirror  No.  1.  <f>  = 44°  59'. 


A 

A 

2 \fj 

n 

K 

6,650 

123°  23' 

88°  49.7' 

0.057 

28.2 

5,893 

116°  26' 

88°  36.7' 

0.059 

22.7 

4,720 

106°  18' 

88°  27.6' 

0.060 

15.5 

1 Any  error  in  this  approximation  is  within  the  limits  of  experimental  error. 


Imp  £ x , or  A* 


OPTICAL  CONSTANTS  OF  SODIUM  AND  POTASSIUM.  307 


Potassium  mirror  No.  2.  <f>  = 44°  59'. 


\ 

A 

2) Jl 

n 

K 

6,650 

128°  29' 

88°  39.0' 

0.075 

25.4 

5,893 

123°  19' 

88°  25.5' 

0.077 

21.6 

4,720 

114°  19' 

88°  5.2' 

0.079 

13.1 

Averages,  etc. 


\ 

n 

K 

<t> 

R 

6,650 

0.066 

26.8 

65°  27' 

43°  56' 

93.8 

5,893 

0.068 

22.1 

62°  58' 

43°  42' 

92.0 

4,720 

0.070 

14.3 

57°  9' 

43°  0' 

86.9 

Although  the  two  potassium  mirrors  studied  seemed  to  be  entirely 
free  from  the  oxide  film,  the  results  are  not  considered  conclusive  until 
more  surfaces  have  been  examined.  No  explanation  is  offered,  at  present , 
for  the  difference  in  the  results  obtained  from  the  two  specimens. 


■i, C 


The  variations  of  the  optical  constants  with  wave-length  are  shown  in 
Figs.  7 and  8.  The  curve  for  the  index  of  refraction  of  sodium  has  a 
distinct  minimum  near  the  D-line. 


Conclusions. 

1.  It  is  possible  to  obtain  and  preserve  indefinitely  bright  surfaces  of 
both  sodium  and  potassium. 

2.  Metallic  sodium  has  the  lowest  index  of  refraction  and  the  highest 
reflecting  power  of  any  metal  known.  This  is  in  agreement  with  Drude’s 
observations.  It  is  interesting  to  note  that  the  value  for  the  refractive 
index  for  sodium  light  is  very  near  (slightly  less  than)  the  upper  limit 
set  by  Drude. 


3°8 


R.  W.  AND  R.  C.  DUNCAN. 


Second 

Series. 


3.  While  the  refractive  index  for  sodium  is  very  low  for  all  wave- 
lengths, it  apparently  has  a minimum  close  to  the  sodium  line. 

4.  Next  to  sodium,  potassium  has  the  lowest  index  of  any  metal. 
Its  reflecting  power,  however,  is  slightly  less  than  that  of  either  silver 
or  sodium. 

5.  The  method  seems  applicable  to  the  sodium-potassium  alloy,  and 
possibly  may  be  adapted  to  other  highly  oxidizable  substances.  By 
using  quartz,  or  uviol  glass,  plates  and  prisms  the  investigation  may  be 
carried  into  the  ultra-violet  by  means  of  Minor’s  method.1 

While  the  results  reported  above  seem  to  be  fairly  consistent  among 
themselves,  the  authors  intend  to  verify  them  by  further  investigation. 
They  hope,  also,  to  be  able  to  determine  the  optical  properties  of  the 
sodium-potassium  alloys,  and  probably  of  some  other  substances,  to 
which  the  same  method  is  applicable. 

In  conclusion  we  wish  to  acknowledge  our  indebtedness  to  Professor 
Arthur  W.  Goodspeed,  who  placed  at  our  disposal  all  the  facilities  of  the 
laboratory  and  kindly  procured  for  us  additional  apparatus.  We  wish 
also  to  thank  Professor  Horace  C.  Richards  for  suggesting  the  subject  of 
this  research  and  for  his  continued  interest  and  cooperation. 

Randal  Morgan  Laboratory  of  Physics, 

University  of  Pennsylvania, 

May,  1912. 

1 Ann.  d.  Phys.,  Vol.  10,  p.  581,  1903. 


